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A080930 2^(n-3)*(n+2)*(n+3)*(n+4)/3. 6
1, 5, 20, 70, 224, 672, 1920, 5280, 14080, 36608, 93184, 232960, 573440, 1392640, 3342336, 7938048, 18677760, 43581440, 100925440, 232128512, 530579456, 1205862400, 2726297600, 6134169600, 13740539904, 30651973632, 68115496960 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Old definition was "Sequence associated with recurrence a(n)=2*a(n-1)+k(k+2)*a(n-2)". See the first comment in A080928.

The fourth column of triangle A080928 (after 0) is 4*a(n).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Index entries for linear recurrences with constant coefficients, signature (8,-24,32,-16).

FORMULA

G.f.: (1-x)*(1-2*x+2*x^2)/(1-2*x)^4 = (1-3*x+4*x^2-2*x^3)/(1-2*x)^4.

a(n) = binomial(n+3,3)*2^(n-3). - Zerinvary Lajos, Oct 29 2006

a(n) = 8*a(n-1)-24*a(n-2)+32*a(n-3)-16*a(n-4) for n>3, a(0)=1, a(1)=5, a(2)=20, a(3)=70. - Bruno Berselli, Aug 06 2013

MAPLE

[seq (binomial(n+3, 3)*2^(n-3), n=1..27)]; # Zerinvary Lajos, Oct 29 2006

MATHEMATICA

CoefficientList[Series[(1 - x) (1 - 2 x + 2 x^2) / (1 - 2 x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Aug 06 2013 *)

LinearRecurrence[{8, -24, 32, -16}, {1, 5, 20, 70}, 30] (* Bruno Berselli, Aug 06 2013 *)

PROG

(MAGMA) [Binomial(n+3, 3)*2^(n-3): n in [1..30]]; // Vincenzo Librandi, Aug 06 2013

(PARI) a(n)=2^(n-3)*(n+2)*(n+3)*(n+4)/3 \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Cf. A080928.

Sequence in context: A291288 A160549 A089094 * A169792 A000343 A005324

Adjacent sequences:  A080927 A080928 A080929 * A080931 A080932 A080933

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Feb 26 2003

EXTENSIONS

Edited by Bruno Berselli, Aug 06 2013

STATUS

approved

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Last modified July 22 16:42 EDT 2019. Contains 325225 sequences. (Running on oeis4.)